Turning error-reducing quantum turbo codes into error-correcting codes

Christopher Boyd

This thesis investigates the feasibility of utilising classical error-correcting codes in quantum communications, specifically in the entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve a classical information rate that approaches the entanglement-assisted capacity of a depolarising channel. Classical information is transmitted over the quantum channel by means of the superdense coding protocol. Different scenarios for the system are considered, including the noiseless and noisy distribution of initial entanglement resources and the use of higher-order entangled states. The overall transmission model corresponding to each scenario is shown to reduce to a classical, discrete and memoryless channel. The capacities of these equivalent classical channels are derived, and an inherent capacity loss when binary classical error correcting codes are employed is identified, motivating the use of non-binary codes. It is ultimately demonstrated that duo-binary turbo codes outperform binary turbo codes in all investigated scenarios, a result of the former's ability to exploit correlations between the pairs of classical bits communicated via the superdense coding protocol.

Khaled Jebari, Luiz Anet Neto, Ramesh Pyndiah +1 more

In the early nineties, the introduction of turbo codes revolutionized classical error correction. The idea was mainly applied on two types of codes: convolutional turbo codes and turbo product codes. The first type of codes was adapted to quantum error correction which initiated the theory of quantum serial turbo codes. In this paper, we present a theory for quantum block turbo codes, the quantum analog of the second type of turbo codes. We describe their iterative decoding algorithm and simulate their performances on a depolarizing channel for different constituent codes.

Markus Grassl

L.-M. Duan, Guang‐Can Guo

황규호

Sungsik Yoon, Jun Heo

In this paper, we introduce a new error correcting protocol in quantum key distribution. With this method, leakage information during the information reconciliation is reduced and a longer key can be obtained. In order to correct errors on the quantum key, we apply the turbo codes and transmit the parity information over the quantum channel. We compare loss rate of the proposed information reconciliation method with a conventional scheme in quantum key distribution.